How to adapt upload_dir to save files outside of WP uploads folder

This is impossible to do (or at the very least not easy).
The way the uploading process works is that first you upload a file to the media library, and only after the file is in the media library you may associate it with a post.

The usage of the media library is mandatory if you want to use the media workflow, and you are more likely to break something that might not be immediately obvious if you try to avoid it.

If your client do not want to use the media library then he should just upload the files in FTP and insert manually the links. (of course this leads to maintenance nightmare in the long run, which is why wordpress stopped doing things like that about 20 releases ago).